Science Myths

Myth #1: The Maxwellian Velocity Distribution can be measured directly with a flux of a model gas.

In many physics laboratories in schools and universities, the experiment "Maxwellian Velocity Distribution" can be found with a model gas of spheres and measuring the velocity distribution at a flux of the model gas:

REALITY:

But only the flux of the pushed out balls is being measured in this experiment, not the ensemble!

Because a physical flux is, by definition, the integral over the density times velocity (v) normal to the cross section, the velocity distribution of the pushed out balls is the Maxwellian Distribution times v, also called Modified Maxwellian Distribution

const3 *v3 *econst2 *v2 .

This multiplication with v is also necessary for calculating the flow rate . The real velocity distribution is more narrow than the Maxwellian distribution and it's maximum is at a little higher speed; that's the reason why the real velocity distribution is called modified Maxwellian distribution. The correct name of the experiment would therefore be "Modified Maxwellian Distribution". This is also described and verified with many experimental results, e. g. in the journal Physical Review, Volume 99, Number 4, August 15, 1955, pages 1314-1321, article "Velocity Distributions in Pottasium and Thallium Atomic Beams" from R. C. Miller and P. Kusch. See also the book "Fundamentals of Statistical and Thermal Physics" from Frederick Reif, Chapter 7.12 (Effusion). In the german version of this book, "Statistische Physik und Theorie der Wärme", from Frederick Reif, 3. Aufl., ISBN 311011383X, you can find it on page 322.

The reason of the misconcept that the Maxwellian Velocity Distribution can be measured directly with a flux of a model gas has been caused in the middle of the 20th century by some layman, e. g. with the (wrong) article "Modellversuch zur kinetischen Theorie" in Beiträge zum mathematisch-naturwissenschaftlichen Unterricht, Heft 8, März 1962, page 1-22, at page 14. And others have copied the error without a check. There are many examples for similar copy and paste errors, e. g. the length of the Rhine, wich is 1233 km, but almost every source used a length of 1320 km (+87 km) from the middle of the 20th century till 2010, because someone made an error which was copied without a check: http://www.sueddeutsche.de/wissen/940/507105/text/. Another example is the legend of the "very high iron content" of spinach with a value of 35 Milligramm / 100 g, which is only one thenth in reality.

Myth #2: The three-body problem is insoluble.

In many physics books and scripts we can find the statement that the three-body problem is insoluble (except of only few special cases), because Poincaré said so in the late 1800s.

REALITY:

Poincaré did only show that with the mathematical methods he used, an analytic solution for 3-body problem can not be found. Several time later, in 1912, the necessary mathematical methods where developed and the Finnish mathematician Karl Fritiof Sundman proved that there exists an analytically solution: Sundman's theorem

Myth #3: The second law of thermodynamics is necessary for defining the arrow of time.

REALITY:

It's true that an arrow of time can be defined via the second law, but only statistical. And since 1998 it is known that time-reversal symmetry is broken in neutral kaons, which means that neutral kaons do show the arrow of time: http://physicsweb.org/articles/world/11/12/3 and http://bulletin.cern.ch/9847/art1/Text_E.html. It is also known that certain subatomic interactions involving the weak nuclear force do violate the conservation of parity. According to the CPT Theorem, this means they are also time irreversible, like the neutral kaons.

Long before 1998 it was known that Quantum mechanics defines an arrow of time by Quantum decoherence e. g. by a free particle, because in Quantum mechanics a free particle is a deliquescent wave packet:

in non-relativistic Quantum mechanics. So in Quantum mechanics the motion of the center of gravity of a free particle is time-reversal but the deliquescing is not because it depends on t2. Therefore time-reversion, which means changing t to -t does not change the deliquescing, because t2=(-t)2 . Another point is that, because of the Uncertainty principle, the reversal of the deliquescing is not possible in Quantum mechanics. That's why the deliquescing of the wave function of a free particle defines a Quantum mechanic arrow of time. That's also a reason why it's hard to build a quantum computer. Another example of a time irreversible process in Quantum mechanics is the Wave function collapse.

Myth #4: Sometimes a kilo is 1000 and sometimes it is 1024.

A kilo, abbreviated k, usually means 1000 but it is often used as the factor 1024, e. g. here, here and for the file size under a Microsoft operating system. Another example is this list of definitons, from http://imgs.xkcd.com/comics/kilobyte.png :

Before the international standard SI, the kilo has been used long before e. g. for the Kilogram and the kilo was defined by the metric (not binary) system, more than 200 years ago in the proclamation on June 22, 1799: http://en.wikipedia.org/wiki/Metric_system .

b)

Since 1999 the international standard IEC 60027-2 is the official and legal standard for the binary prefixes and defines kibi, abbreviated ki, as 1024. This standard also defines mebi (=1,048,576), gibi (=1,073,741,824), tebi (=1,099,511,627,776) etc.. So the binary prefixes are well-defined by a worldwide standard since more than a decade!

Before IEC 60027-2 and the kibi, 1024 was written as capitalized prefix K, not k, to make clear that it is NOT a kilo (because it was simply "K" and nothing else); setting k to 1024 is therefore completely wrong! An example with the capitalized prefix K is the output of the df command under Unix/Linux (2008):

> df

Filesystem

1K-blocks

Used

Available

Use%

Mounted on

/dev/hda4

332077476

201822772

130254704

61%

/

udev

907756

152

907604

1%

/dev

/dev/hda2

29301628

6730332

22571296

23%

/tmp

/dev/hda3

19542436

3769236

15773200

20%

/var

But that was not a good solution, because the "K" has never been a part of a standard or legal law and the Kelly-Bootle Standard Unit (=1012) uses the same notation! Although for exact countable integer things like bits and bytes it does not make sense to say 1024 is nearly 1000, in many old software and even in 2009 actual operating systems from Microsoft you can find the bug that binary prefixes are confused with decimal prefixes but hardware manufacturers (usually) do use the prefixes correct. An example is the capacity of this old 120 GB IDE hard disk drive, where you can find the correct equation 1 GB=1,000,000,000 Bytes in the middle of the sticker:

It's simple to use binary prefixes when you mean binary prefixes and to use decimal prefixes when you mean decimal prefixes, but because of Dyscalculia some people can't do it and create such crazy things like the 1.44 MB Floppy Disk, where 1000*1024 was used for mega and not 10002 (or 10242).

A remaining problem is that the IEC 60027-2 only defines binary prefixes greater one, because decimal prefixes smaller one are often used and even the good old ANSI-C (C99) has hexadecimal floating-point numbers. An example is the output of an Analog-to-Digital-Converter which is the multiple of 1/1024 Volt: It`s easy to say the output is n Mibivolt (not Millivolt) but it`s not so easy to say the output is n*0.9765625 Millivolt. So it makes sense to use

The binary prefixes greater one are greater than the decimal and the decimal prefixes smaller one are greater than the binary.

Another remaining problem is that the Microsoft operating systems have additional errors, as can be seen in the next picture:

As can be seen in this picture, under MS-Windows XP the newer linux.txt is reported with 238 KB on the disc, with 237 KB in the dialog, and the older linux.txt is reported with 233 KB on the disk and 232 KB in the dialog. So the (reported) file size under MS-Windows XP is context-dependent: In a dialog the files are about 0.5 % smaller, even if they are shown with the same unit (KB which means kiB under MS-Windows XP); the unit "K" is not constant under Microsoft Windows XP.